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Parameter estimation in logistic regression is a well-studied problem with the Newton-Raphson method being one of the most prominent optimization techniques used in practice. A number of monotone optimization methods including…

The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…

Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…

The performance of tracking algorithms strongly depends on the chosen model assumptions regarding the target dynamics. If there is a strong mismatch between the chosen model and the true object motion, the track quality may be poor or the…

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

We study online estimation in latent-variable models by recasting the problem as tracking a moving empirical equilibrium. Standard online EM and stochastic approximation analyses primarily study convergence toward the population parameter…

Expectation maximization (EM) algorithm is to find maximum likelihood solution for models having latent variables. A typical example is Gaussian Mixture Model (GMM) which requires Gaussian assumption, however, natural images are highly…

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive…

Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…

Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex…

The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…

Distributed parameter identification for large-scale multi-agent networks encounters challenges due to nonlinear dynamics and partial observations. Simultaneously, ensuring the stability is crucial for the robust identification of dynamic…

Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…

Unlike the commonly used parametric regression models such as mixed models, that can easily violate the required statistical assumptions and result in invalid statistical inference, target maximum likelihood estimation allows more realistic…

The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…

This paper presents a coordinate ascent algorithm to learn dynamic and measurement models in dynamic state estimation using maximum likelihood estimation in a supervised manner. In particular, the dynamic and measurement models are assumed…

The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…

We consider multitarget detection and tracking problem for a class of multipath detection system where one target may generate multiple measurements via multiple propagation paths, and the association relationship among targets,…